1a. There are 2^25 possible 5x5 patterns. In the general case, there are 2^(MN) patterns.
1b. There are a number of possibilities, assuming that a unit-cost move consists of changing one square from black to white (or vice versa). Here are a few reasonable h-functions -- note that each of these cannot overestimate the true cost of a path to the solution.
Number of rows (or columns) whose goal number is different from the current number of black squares.
Sum of error-values for each row (where "error-value" is the absolute value of the difference between the goal and the current number of black squares in the row).
Sum of error-values for each column.
Sum of all row- and column-error-values divided by 2.
2a. The value to MAX of the tree is 3.
2b. The leaves that are examined are: 3, 1, 6, 2, and 0. The others are cut off by alpha-beta pruning.
Qualitatively, this is about what you'd expect: Sparky's bad mood suggests that the Rockies probably lost today.